Population Dynamics Model Research Articles

A Model for Estimating Final Clutch Size from Follicle Counts in Plethodontid Salamanders

Estimates of clutch sizes are essential for modeling population dynamics, yet for many species of amphibian, clutches can be difficult to observe or methodologically problematic to measure. Clutch sizes for direct-developing Plethodontidae are regularly estimated from counts of ovarian follicles. Because many more follicles begin to develop in an ovary than will ultimately reach full size and be deposited, follicle counts change dramatically over an individual female's follicle development cycle, and a high level of subjectivity is inherent in the process of estimating clutch sizes from follicle counts. Many published studies are not transparent in how they determine clutch sizes from follicle counts. Some investigators address this bias using threshold sizes or other characteristics to separate those follicles that will ultimately mature and be deposited from those that will not, but our experience indicates that such approaches still likely overestimate clutch sizes. To move beyond the subjectivity inherent in estimation of final clutch size from follicle counts, we modeled large Plethodon clutch size as a function of female body size (snout–vent length, SVL) and follicle diameter, then used that model to predict the likely number of mature eggs deposited. We propose that this approach provides reasonable estimates of clutch sizes and variances for use in demographic models.

Nonlinear optimal control of a mean-field model of neural population dynamics.

We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is defined by two alternative cost functions that trade the deviation of the controlled variable from its target value against the “strength” of the control, which is quantified by the integrated 1- and 2-norms of the control signal. We focus on a bistable region in state space where one low- (“down state”) and one high-activity (“up state”) stable fixed points coexist. With methods of nonlinear optimal control, we search for the most cost-efficient control function to switch between both activity states. For a broad range of parameters, we find that cost-efficient control strategies consist of a pulse of finite duration to push the state variables only minimally into the basin of attraction of the target state. This strategy only breaks down once we impose time constraints that force the system to switch on a time scale comparable to the duration of the control pulse. Penalizing control strength via the integrated 1-norm (2-norm) yields control inputs targeting one or both populations. However, whether control inputs to the excitatory or the inhibitory population dominate, depends on the location in state space relative to the bifurcation lines. Our study highlights the applicability of nonlinear optimal control to understand neuronal processing under constraints better.

Quantification of spatial subclonal interactions enhancing the invasive phenotype of pediatric glioma.

SummaryDiffuse midline gliomas (DMGs) are highly aggressive, incurable childhood brain tumors. They present a clinical challenge due to many factors, including heterogeneity and diffuse infiltration, complicating disease management. Recent studies have described the existence of subclonal populations that may co-operate to drive pro-tumorigenic processes such as cellular invasion. However, a precise quantification of subclonal interactions is lacking, a problem that extends to other cancers. In this study, we combine spatial computational modeling of cellular interactions during invasion with co-evolution experiments of clonally disassembled patient-derived DMG cells. We design a Bayesian inference framework to quantify spatial subclonal interactions between molecular and phenotypically distinct lineages with different patterns of invasion. We show how this approach could discriminate genuine interactions, where one clone enhanced the invasive phenotype of another, from those apparently only due to the complex dynamics of spatially restricted growth. This study provides a framework for the quantification of subclonal interactions in DMG.

Open removal models with temporary emigration and population dynamics to inform invasive animal management.

Removal sampling data are the primary source of monitoring information for many populations (e.g., invasive species, fisheries). Population dynamics, temporary emigration, and imperfect detection are common sources of variation in monitoring data and are key parameters for informing management. We developed two open robust‐design removal models for simultaneously modeling population dynamics, temporary emigration, and imperfect detection: a random walk linear trend model (estimable without ancillary information), and a 2‐age class informed population model (InfoPM, closely related to integrated population models) that incorporated prior information for age‐structured vital rates and relative juvenile availability. We applied both models to multiyear, removal trapping time‐series of a large invasive lizard (Argentine black and white tegu, Salvator merianae) in three management areas of South Florida to evaluate the effectiveness of management programs. Although estimates of the two models were similar, the InfoPMs generally returned more precise estimates, partitioned dynamics into births, deaths, net migration, and provided a decision support tool to predict population dynamics under different effort scenarios while accounting for uncertainty. Trends in tegu superpopulation abundance estimates were increasing in two management areas despite generally high removal rates. However, tegu abundance appeared to decline in the Core management area, where trapping density was the highest and immigration the lowest. Finally, comparing abundance predictions of no‐removal scenarios to those estimated in each management area suggested significant population reductions due to management. These results suggest that local tegu population control via systematic trapping may be feasible with high enough trap density and limited immigration; and highlights the value of these trapping programs. We provided the first estimates of tegu abundance, capture probabilities, and population dynamics, which is critical for effective management. Furthermore, our models are applicable to a wide range of monitoring programs (e.g., carcass recovery or removal point‐counts).

Cheater suppression and stochastic clearance through quorum sensing.

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected effects of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the growth rate of populations in the absence of public goods. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

Competition for pollinators destabilizes plant coexistence.

Mounting concern over the global decline of pollinators has fuelled calls for investigating their role in maintaining plant diversity1,2. Theory predicts that competition for pollinators can stabilize interactions between plant species by providing opportunities for niche differentiation3, while at the same time can drive competitive imbalances that favour exclusion4. Here we empirically tested these contrasting effects by manipulating competition for pollinators in a way that predicts its long-term implications for plant coexistence. We subjected annual plant individuals situated across experimentally imposed gradients in neighbour density to either ambient insect pollination or a pollen supplementation treatment alleviating competition for pollinators. The vital rates of these individuals informed plant population dynamic models predicting the key theoretical metrics of species coexistence. Competition for pollinators generally destabilized the interactions between plant species, reducing the proportion of pairs expected to coexist. Interactions with pollinators also influenced the competitive imbalances between plant species, effects that are expected to strengthen with pollinator decline, potentially disrupting plant coexistence. Indeed, results from an experiment simulating pollinator decline showed that plant species experiencing greater reductions in floral visitation also suffered greater declines in population growth rate. Our results reveal that competition for pollinators may weaken plant coexistence by destabilizing interactions and contributing to competitive imbalances, information critical for interpreting the impacts of pollinator decline.

Combining food web theory and population dynamics to assess the impact of invasive species

The impacts of invasive species on resident communities are driven by a tangle of ecological interactions difficult to quantify empirically. Combining a niche model with a population dynamic model, both allometrically parametrized, may represent a consistent framework to investigate invasive species impacts on resident communities in a food web context when empirical data are scarce. We used this framework to assess the ecological consequences of an invasive apex predator (Silurus glanis) in peri-Alpine lake food webs. Both increases and decreases of resident species abundances were highlighted and differed when accounting for differentS. glanisbody sizes. Complementarily, the prominence of indirect effects, such as trophic cascades, suggested that common approaches may only capture a restricted fraction of invasion consequences through direct predation or competition. By leveraging widely available biodiversity data, our approach may provide relevant insights for a comprehensive assessment and management of invasive species impacts on aquatic ecosystems.

Emergence dynamics of adult Culicoides biting midges at two farms in south-east England

BackgroundCulicoides biting midges (Diptera: Ceratopogonidae) are biological vectors of livestock arboviruses that cause diseases with significant economic, social and welfare impacts. Within temperate regions, livestock movement during arbovirus outbreaks can be facilitated by declaring a ‘seasonal vector-free period’ (SVFP) during winter when adult Culicoides are not active. In this study we carry out long-term monitoring of Culicoides adult emergence from larval development habitats at two farms in the UK to validate current definitions of the SVFP and to provide novel bionomic data for known vector species.MethodsStandard emergence traps were used to collect emerging adult Culicoides from dung heaps at two cattle farms in the south-east of England from June to November 2016 and March 2017 to May 2018. Culicoides were morphologically identified to species or complex level and count data were analysed using a simple population dynamic model for pre-adult Culicoides that included meteorological components.ResultsMore than 96,000 Culicoides were identified from 267 emergence trapping events across 2 years, revealing clear evidence of bivoltinism from peaks of male populations of Culicoidesobsoletus emerging from dung heaps. This pattern was also reflected in the emergence of adult female Obsoletus complex populations, which dominated the collections (64.4% of total catch) and emerged throughout the adult active period. Adult male C. obsoletus were observed emerging earlier than females (protandry) and emergence of both sexes occurred throughout the year. Culicoides chiopterus and Culicoides scoticus were also identified in spring emergence collections, providing the first evidence for the overwintering of larvae in dung heaps for these species.ConclusionsThis study demonstrates continual and highly variable rates of emergence of Culicoides throughout the year. A lack of evidence for mass emergence in spring along with the ability to observe male generations highlights the need for complementary surveillance techniques in addition to light-trap data when investigating seasonality and phenology. Evidence was found of other vector species, C. chiopterus and C. scoticus, utilising cattle dung heaps as an overwintering habitat, further highlighting the importance of these habitats on farms.Graphical

Declines in Pregnancies among U.S. Adolescents from 2007 to 2017: Behavioral Contributors to the Trend

Adolescent pregnancies and births in the United States have undergone dramatic declines in recent decades. We aimed to estimate the contribution of changes in 3 proximal behaviors to these declines among 14- to 18-year-olds for 2007-2017: 1) delays in age at first sexual intercourse, 2) declines in number of sexual partners, and 3) changes in contraceptive use, particularly uptake of long-acting reversible contraception (LARC). We adapted an existing iterative dynamic population model and parameterized it using 6 waves of the Centers for Disease Control and Prevention's Youth Risk Behavior Survey. We compared pregnancies from observed behavioral trends with counterfactual scenarios that assumed constant behaviors over the decade. We calculated outcomes by cause, year, and age. We found that changes in these behaviors could explain pregnancy reductions of 496,200, 78,500, and 40,700 over the decade, respectively, with total medical and societal cost savings of $9.71 billion, $1.54 billion, and $796 million. LARC adoption, particularly among 18-year-olds, could explain much of the improvement from contraception use. The 3 factors together did not fully explain observed birth declines; adding a 50% decline in sex acts per partner did. Delays in first sexual intercourse contributed the most to declining births over this decade, although all behaviors considered had major effects. Differences from earlier models could result from differences in years and ages covered. Evidence-based teen pregnancy prevention programs, including comprehensive sex education, youth-friendly reproductive health services, and parental and community support, can continue to address these drivers and reduce teen pregnancy.

A dynamically structured matrix population model for insect life histories observed under variable environmental conditions

Various environmental drivers influence life processes of insect vectors that transmit human disease. Life histories observed under experimental conditions can reveal such complex links; however, designing informative experiments for insects is challenging. Furthermore, inferences obtained under controlled conditions often extrapolate poorly to field conditions. Here, we introduce a pseudo-stage-structured population dynamics model to describe insect development as a renewal process with variable rates. The model permits representing realistic life stage durations under constant and variable environmental conditions. Using the model, we demonstrate how random environmental variations result in fluctuating development rates and affect stage duration. We apply the model to infer environmental dependencies from the life history observations of two common disease vectors, the southern (Culex quinquefasciatus) and northern (Culex pipiens) house mosquito. We identify photoperiod, in addition to temperature, as pivotal in regulating larva stage duration, and find that carefully timed life history observations under semi-field conditions accurately predict insect development throughout the year. The approach we describe augments existing methods of life table design and analysis, and contributes to the development of large-scale climate- and environment-driven population dynamics models for important disease vectors.

Density or variability: is it time for a paradigm shift in ecology?

In ecology, the paradigm of density is commonly used. It is used to construct mathematical models and to plan and interpret ecological experiments. This leads to mathematical models using differential equations in ecology. It seems, however, due the fundamental discontinuity in ecological systems, which appears in the form of discrete individuals in the population, we should use in models of population dynamics a paradigm that speaks of the variability of these individuals and the discontinuity of basic demographic processes in populations. This should result in the further development of individual-based modelling in ecology as well as the development of experimental individual-based ecology. The paradigm of dependence on density in a slightly altered form and the assumption of the continuity of ecological processes can continue to be used in those branches of ecology that deal with the cycling of matter and the flow of energy through ecological systems.

Large-scale PVA modeling of insects in cultivated grasslands: The role of dispersal in mitigating the effects of management schedules under climate change.

In many species, dispersal is decisive for survival in a changing climate. Simulation models for population dynamics under climate change thus need to account for this factor. Moreover, large numbers of species inhabiting agricultural landscapes are subject to disturbances induced by human land use. We included dispersal in the HiLEG model that we previously developed to study the interaction between climate change and agricultural land use in single populations. Here, the model was parameterized for the large marsh grasshopper (LMG) in cultivated grasslands of North Germany to analyze (1) the species development and dispersal success depending on the severity of climate change in subregions, (2) the additional effect of grassland cover on dispersal success, and (3) the role of dispersal in compensating for detrimental grassland mowing. Our model simulated population dynamics in 60‐year periods (2020–2079) on a fine temporal (daily) and high spatial (250 × 250 m2) scale in 107 subregions, altogether encompassing a range of different grassland cover, climate change projections, and mowing schedules. We show that climate change alone would allow the LMG to thrive and expand, while grassland cover played a minor role. Some mowing schedules that were harmful to the LMG nevertheless allowed the species to moderately expand its range. Especially under minor climate change, in many subregions dispersal allowed for mowing early in the year, which is economically beneficial for farmers. More severe climate change could facilitate LMG expansion to uninhabited regions but would require suitable mowing schedules along the path. These insights can be transferred to other species, given that the LMG is considered a representative of grassland communities. For more specific predictions on the dynamics of other species affected by climate change and land use, the publicly available HiLEG model can be easily adapted to the characteristics of their life cycle.

Intelligent Decision-Support System for Epidemiological Diagnostics. II. Information Technologies Development*, *.

The article projects the components of the intelligent decision support system for epidemiological diagnostics and investigates their interaction with the user. The system includes a bank of models and machine learning methods, a bank of population dynamics models, visualization and reporting tools, and management decision-making unit. The concept of information technology to ensure biosafety of the population is provided. A model of specified information technology use cases is developed and a sequence diagram is constructed. A model of information technology components and ways of their deployment on a server are proposed.

Analyzing dynamic species abundance distributions using generalized linear mixed models.

Understanding the mechanisms of ecological community dynamics and how they could be affected by environmental changes is important. Population dynamic models have well known ecological parameters that describe key characteristics of species such as the effect of environmental noise and demographic variance on the dynamics, the long‐term growth rate, and strength of density regulation. These parameters are also central for detecting and understanding changes in communities of species; however, incorporating such vital parameters into models of community dynamics is challenging. In this paper, we demonstrate how generalized linear mixed models specified as intercept‐only models with different random effects can be used to fit dynamic species abundance distributions. Each random effect has an ecologically meaningful interpretation either describing general and species‐specific responses to environmental stochasticity in time or space, or variation in growth rate and carrying capacity among species. We use simulations to show that the accuracy of the estimation depends on the strength of density regulation in discrete population dynamics. The estimation of different covariance and population dynamic parameters, with corresponding statistical uncertainties, is demonstrated for case studies of fish and bat communities. We find that species heterogeneity is the main factor of spatial and temporal community similarity for both case studies.

Accounting for Errors in Data Improves Divergence Time Estimates in Single-cell Cancer Evolution.

Single-cell sequencing provides a new way to explore the evolutionary history of cells. Compared to traditional bulk sequencing, where a population of heterogeneous cells is pooled to form a single observation, single-cell sequencing isolates and amplifies genetic material from individual cells, thereby preserving the information about the origin of the sequences. However, single-cell data are more error-prone than bulk sequencing data due to the limited genomic material available per cell. Here, we present error and mutation models for evolutionary inference of single-cell data within a mature and extensible Bayesian framework, BEAST2. Our framework enables integration with biologically informative models such as relaxed molecular clocks and population dynamic models. Our simulations show that modeling errors increase the accuracy of relative divergence times and substitution parameters. We reconstruct the phylogenetic history of a colorectal cancer patient and a healthy patient from single-cell DNA sequencing data. We find that the estimated times of terminal splitting events are shifted forward in time compared to models which ignore errors. We observed that not accounting for errors can overestimate the phylogenetic diversity in single-cell DNA sequencing data. We estimate that 30–50% of the apparent diversity can be attributed to error. Our work enables a full Bayesian approach capable of accounting for errors in the data within the integrative Bayesian software framework BEAST2.

Emergence of networks of shared restriction-modification systems in phage–bacteria ecosystems

Restriction-modification (RM) systems are the most ubiquitous bacterial defence systems against bacteriophages. Using genome sequence data, we showed that RM systems are often shared among bacterial strains in a structured way. Examining the network of interconnections between bacterial strains within genera, we found that many strains share more RM systems than expected compared with a suitable null model. We also found that many genera have a larger than expected number of bacterial strains with unique RM systems. We used population dynamics models of closed and open phage-bacteria ecosystems to qualitatively understand the selection pressures that could lead to such network structures with enhanced overlap or uniqueness. In our models, we found that the phages impose a selection pressure that favours bacteria with greater number of RM systems, and higher overlap of RM systems with other strains, but in bacteria-dominated states, this is opposed by the increased cost-to-growth rate of these bacteria. Similar to what we observed in the genome data, we found that two distinct bacterial strategies emerge - strains either have a greater overlap than expected, or, at the other extreme, have unique RM systems. The former strategy appears to dominate when the repertoire of available RM systems is smaller but the average number of RM systems per strain is larger.

A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

This study concentrates on the dynamics of a prey–predator model incorporating the fear effect in the birth and death rate of prey, whose physiological changes may give rise to undirect predation. In the presence and absence of time delay, single parameter numerical continuation with respect to two parameters, that are (i) fear level in the death rate of prey and (ii) conversion efficiency by which new predators are introduced through prey consumption in the system, is performed. Basic results on extinction and delay‐driven Hopf bifurcation criteria are investigated. Then, the model is extended to involve the spatial dynamics with and without time delay. Theoretical results for orientation and stability of Hopf bifurcation in spatial system are provided by applying the normal form recipe and also the center manifold theory. Classical reaction–diffusion‐type models, incorporating self‐diffusion, can induce regular (periodic) and irregular (chaotic) oscillations in space. However, space periodic oscillations are not common in prey–predator interactions. Here, it is shown that the dynamics of only diffusion involved model is periodically arranged in space and time. However, introducing a very small value of time delay in predator maturation, spatial dynamics with chaos is initiated as a result of the joint effect of time delay and diffusion. This reassures that time delay has a crucial role in population dynamics incorporated with the role of indirect predation and gives some useful intuition into underlying species interactions. Theoretical results of the model in this paper are supported with numerical experiments.

Sufficient Conditions for the Existence and Uniqueness of the Solution of the Dynamics of Biogeochemical Cycles in Coastal Systems Problem

The article considers a three-dimensional mathematical model of population dynamics based on a system of non-stationary parabolic advection-diffusion-reaction equations with lower derivatives describing the advective motion of the aquatic environment and non-linear source functions. In contrast to the previous authors’ works devoted to the description of this model and its numerical implementation, this article presents the results of an analytical study of the initial-boundary value problem corresponding to this model. For these purposes, the original initial-boundary value problem is linearized on a single time grid—for all nonlinear sources, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial—final data at each step of the time grid. For this chain of linearized problems, the existence and uniqueness of the solution of the initial-boundary value problem for the system of partial differential equations in the Hilbert space were researched. Numerical experiments were performed for model problems of the main types of phytoplankton populations in coastal systems under the influence of dynamically changing biotic and abiotic factors, the results of which are consistent with real physical experiments. The developed model, including the proposed model of biological kinetics, allows for the study of the productive and destructive processes of the shallow water body biocenosis to assess the state of the processes of reproduction of valuable and commercial fish participating in the food chain with selected species of summer phytoplankton.

Simple Mechanisms of Plant Reproductive Benefits Yield Different Dynamics in Pollination and Seed Dispersal Mutualisms.

AbstractPollination and seed dispersal mutualisms are critical for biodiversity and ecosystem services yet face mounting threats from anthropogenic perturbations that cause their populations to decline. Characterizing the dynamics of these mutualisms when populations are at low density is important to anticipate consequences of these perturbations. We developed simple population dynamic models detailed enough to distinguish different mechanisms by which plant populations benefit from animal pollination or seed dispersal. We modeled benefits as functions of foraging rate by animals on plant rewards and specified whether they affected plant seed set, germination, or negative density dependence during recruitment. We found that pollination and seed dispersal mutualisms are stable at high density but exhibit different dynamics at low density, depending on plant carrying capacity, animal foraging efficiency, and whether populations are obligate on their partners for persistence. Under certain conditions, all mutualisms experience destabilizing thresholds in which one population declines because its partner is too rare. Plants additionally experience Allee effects when obligate on pollinators. Finally, pollination mutualisms can exhibit bistable coexistence at low or high density when plants are facultative on pollinators. Insights from our models can inform conservation efforts, as mutualist populations continue to decline globally.

A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory

This paper deals with a model of population dynamics comprising Allee effect and weakening memory with constant time delays. Since predator density depends on the prey density in current time and in past, a two-component model of prey-predator interactions is complemented with a third differential equation for the influence of recent past. The role of constant time delays incorporated in the functional form of Allee effect (referred as delays in competition and cooperation) is investigated analytically and numerically. Steady states of the model are obtained and the local stability analysis around the coexisting state is calculated in the presence of both delays. The critical threshold for time delays, above which the stability of the system switches from stable (unstable) to unstable (stable), is computed for various cases. Analytical findings of this paper are supported with numerical simulations, where time evolution as well as numerical bifurcation diagrams are presented. The results of this paper demonstrate that the influence of past on the prey-predator density in the present of time delay may have a considerable effect upon the system behaviour and can give important insights into underlying biological mechanism.