Population Growth Model Research Articles

Host-pathogen immune feedbacks can explain widely divergent outcomes from similar infections.

A long-standing question in infection biology is why two very similar individuals, with very similar pathogen exposures, may have very different outcomes. Recent experiments have found that even isogenic Drosophila melanogaster hosts, given identical inoculations of some bacterial pathogens at suitable doses, can experience very similar initial bacteria proliferation but then diverge to either a lethal infection or a sustained chronic infection with much lower pathogen load. We hypothesized that divergent infection outcomes are a natural result of mutual negative feedbacks between pathogens and the host immune response. Here, we test this hypothesis in silico by constructing process-based dynamic models for bacterial population growth, host immune induction and the feedbacks between them, based on common mechanisms of immune system response. Mathematical analysis of a minimal conceptual model confirms our qualitative hypothesis that mutual negative feedbacks can magnify small differences among hosts into life-or-death differences in outcome. However, explaining observed features of chronic infections requires an extension of the model to include induced pathogen modifications that shield themselves from host immune responses at the cost of reduced proliferation rate. Our analysis thus generates new, testable predictions about the mechanisms underlying bimodal infection outcomes.

Global asymptotic properties of a stochastic model of population growth

In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the current population size. Using the direct Lyapunov method, we established the global properties of this stochastic differential equation. In particular, we found that solutions with positive initial conditions converge to a certain bounded region in the model phase space and oscillate around this region thereafter. Moreover, we found that, if the magnitude of the noise exceeds a certain critical level (which is also explicitly found), then the stochastic stabilization (“stabilization by noise”) of the zero solution occurs. In this case, (i) the origin is the lower boundary of the interval, and (ii) the extinction of the population due to stochasticity occurs almost sure (a.s.) for a finite time.

Population growth model of the carob moth, Ectomyelois ceratoniae (Lepidoptera: Pyralidae) under field conditions

The carob moth, Ectomyelois ceratoniae Zeller, is the most important pest on pomegranate fruits and has several overlapping generations per year in Iran. This paper investigated the use of a mechanistic model for describing the effect of the control strategy on the size of the total population of the carob moth. The analytical solution of mechanistic model was written in the form of a logistic probability density function by Matis et al. (2006). The logistic probability density function fits this carob moth data very well for control and treatment fields (r2=0.91 and 0.95). The parameters of the model are the predicted peak size, Nmax, the predicted time of peak, tmax, and an approximate per capita birth and death rate, all of which are important in practical application. In general, this paper demonstrates the utility of analyzing carob moth population data using mechanistic models and their underlying rate parameters.

Microhabitats associated with solar energy development alter demography of two desert annuals.

Political and economic initiatives intended to increase energy production while reducing carbon emissions are driving demand for solar energy. Consequently, desert regions are now targeted for development of large‐scale photovoltaic solar energy facilities. Where vegetation communities are left intact or restored within facilities, ground‐mounted infrastructure may have negative impacts on desert‐adapted plants because it creates novel rainfall runoff and shade conditions. We used experimental solar arrays in the Mojave Desert to test how these altered conditions affect population dynamics for a closely related pair of native annual plants: rare Eriophyllum mohavense and common E. wallacei. We estimated aboveground demographic rates (seedling emergence, survivorship, and fecundity) over 7 yr and used seed bank survival rates from a concurrent study to build matrix models of population growth in three experimental microhabitats. In drier years, shade tended to reduce survival of the common species, but increase survival of the rare species. In a wet year, runoff from panels tended to increase seed output for both species. Population growth projections from microhabitat‐specific matrix models showed stronger effects of microhabitat under wetter conditions, and relatively little effect under dry conditions (lack of rainfall was an overwhelming constraint). Performance patterns across microhabitats in the wettest year differed between rare and common species. Projected growth of E. mohavense was substantially reduced in shade, mediated by negative effects on aboveground demographic rates. Hence, the rare species were more susceptible to negative effects of panel infrastructure in wet years that are critical to seed bank replenishment. Our results suggest that altered shade and water runoff regimes associated with energy infrastructure will have differential effects on demographic transitions across annual species and drive population‐level processes that determine local abundance, resilience, and persistence.

A Bayesian approach for fitting and comparing demographic growth models of radiocarbon dates: A case study on the Jomon-Yayoi transition in Kyushu (Japan).

Large sets of radiocarbon dates are increasingly used as proxies for inferring past population dynamics and the last few years, in particular, saw an increase in the development of new statistical techniques to overcome some of the key challenges imposed by this kind of data. These include: 1) null hypothesis significance testing approaches based on Monte-Carlo simulations or mark permutations; 2) non-parametric Bayesian modelling approaches, and 3) the use of more traditional techniques such as correlation, regression, and AIC-based model comparison directly on the summed probability distribution of radiocarbon dates (SPD). While the range of opportunities offered by these solutions is unquestionably appealing, they often do not consider the uncertainty and the biases arising from calibration effects or sampling error. Here we introduce a novel Bayesian approach and nimbleCarbon, an R package that offers model fitting and comparison for population growth models based on the temporal frequency data of radiocarbon dates. We evaluate the robustness of the proposed approach on a range of simulated scenarios and illustrate its application on a case study focused on the demographic impact of the introduction of wet-rice farming in prehistoric Japan during the 1st millennium BCE.

Demographic impact of landfill closure on a resident opportunistic gull

AbstractThe management of mixed municipal waste can have an impact on wildlife and ecosystems. Previous studies have investigated how opportunistic species like gulls can react very fast to new landfills; however, the impact of landfill closure on bird populations is less investigated. Yet, there is a need to understand how fast and to what extent, animal populations can be adapted to new scenarios where the waste will not be deposited in landfill sites anymore. The aim is to determine the influence of landfill closures on apparent survival of a resident Yellow‐legged Gull (Larus michahellis) population, used as a model species showing short‐distance foraging movements, and with a high dependence on local food subsidies. Complementarily, we built some basic population growth models in order to determine how potential changes in survival (before/after landfill closure) will impact on population growth rate. Using a data set of 4,437 Yellow‐legged Gull chicks ringed in four colonies over a period of 13 years, we obtained evidence supporting that the apparent survival was affected by landfill closure, especially if the landfill was located within a buffer of 10 km around the colony. Landfill closure affected the survival of first‐year gulls (with a mean decrease of ~ 0.5–0.36), but not of older birds. Consequently, we did not detect a remarkable effect of landfill closures on population growth rate, probably due to the lack of effect on adult survival rates except for one of the surveyed colonies, where we found an annual decline of 7%.

A cubic nonlinear population growth model for single species: theory, an explicit\u2013implicit solution algorithm and applications

In this paper, we extend existing population growth models and propose a model based on a nonlinear cubic differential equation that reveals itself as a special subclass of Abel differential equations of first kind. We first summarize properties of the time-continuous problem formulation. We state the boundedness, global existence, and uniqueness of solutions for all times. Proofs of these properties are thoroughly given in the Appendix to this paper. Subsequently, we develop an explicit–implicit time-discrete numerical solution algorithm for our time-continuous population growth model and show that many properties of the time-continuous case transfer to our numerical explicit–implicit time-discrete solution scheme. We provide numerical examples to illustrate different behaviors of our proposed model. Furthermore, we compare our explicit–implicit discretization scheme to the classical Eulerian discretization. The latter violates the nonnegativity constraints on population sizes, whereas we prove and illustrate that our explicit–implicit discretization algorithm preserves this constraint. Finally, we describe a parameter estimation approach to apply our algorithm to two different real-world data sets.

Drivers of depopulation and spatial interdependence in a regional context

There is a growing consensus on the need to propose specific policies to tackle the ongoing population decline in extensive rural areas of Southern Europe. Developing policies to target this issue requires assessment of the spatial, economic and structural conditions that explain why a municipality experiences depopulation. This study explores the drivers of population growth in the municipalities of the Mediterranean region officially known as the Comunitat Valenciana in Spain. This region is relatively urbanized, so the study allows to explore the spatial interdependence between municipalities that belong to urban and rural areas, some of them subject to significant depopulation. The study's findings, based on a spatial approach, help explain the population growth of municipalities based on their interdependence with neighbouring communities. A population growth model is defined drawing on several dimensions related to population dynamics: accessibility, economic conditions, public facilities and services, natural amenities, and degree of urbanization. The findings show that population dynamics in a given municipality are influenced by its surrounding municipalities, suggesting that policies focusing on clusters of local administrative units can be central to prevent the depopulation of certain areas.

Re-introduction of the Saker Falcon (Falco cherrug) in Bulgaria - preliminary results from the ongoing establishment phase by 2020.

Considered extinct as breeding species in the early 2000s, the Saker Falcon was recovered when the first active nest from the new history of the species in Bulgaria was discovered in 2018, formed of two birds that were re-introduced back in 2015. Currently, there is only one confirmed wild breeding pair in the country - the male from 2015 with a female changed in 2020, released again as a part of the programme, in 2016. This is a report on the preliminary results and analysis of the ongoing establishment phase of the re-introduction of the Saker Falcon (Falco cherrug) in Bulgaria - first ever performed for this species in the country and globally. The period studied is 2015-2020. Following the re-introduction activities started in 2011, the current phase is defined by standardised methodology and a unified approach. Analysed and presented are methods for captive breeding and hacking, the breeding performance of the falcons, the number of released individuals, data from the post-fledging dependence period and a model of population growth.

Optimal Sampling Regimes for Estimating Population Dynamics

Ecologists are interested in modeling the population growth of species in various ecosystems. Specifically, logistic growth arises as a common model for population growth. Studying such growth can assist environmental managers in making better decisions when collecting data. Traditionally, ecological data is recorded on a regular time frequency and is very well-documented. However, sampling can be an expensive process due to available resources, money and time. Limiting sampling makes it challenging to properly track the growth of a population. Thus, this design study proposes an approach to sampling based on the dynamics associated with logistic growth. The proposed method is demonstrated via a simulation study across various theoretical scenarios to evaluate its performance in identifying optimal designs that best estimate the curves. Markov Chain Monte Carlo sampling techniques are implemented to predict the probability of the model parameters using Bayesian inference. The intention of this study is to demonstrate a method that can minimize the amount of time ecologists spend in the field, while maximizing the information provided by the data.

Using environmental variation to optimize aerial surveys of harbour seals

Abstract Harbour seals are surveyed aerially when they haul-out to moult in August. The proportion of the population hauled out throughout the year is related to temporal, environmental, and meteorological variables. Thus, monitoring is conducted under predefined ranges of conditions. Effects of variation within these ranges are rarely reviewed. We used linear models to assess effects of time, date and weather on the difference between counts predicted by a population growth model and observed counts, based on a 30-year time-series. Our top-ranked model explained 34.4% of the variance. Survey date and its interaction with survey year were the most important variables, with higher counts earlier in August, particularly early in the time series, where surveys may not have been timed optimally to capture the peak in the moult. Cloud cover, wind speed, temperature, and interactions between these were of lesser importance; there were fewer seals on land during cloudy, windy days and on clear, warm days. These effects of weather are likely related to temperature regulation. Power analyses suggested that correction for survey conditions would allow detection of a one percentage point annual change in population growth rate with 80% power 4 years sooner than without taking survey conditions into account.

Aplikasi Persamaan Diferensial Dalam Mengestimasi Jumlah Penduduk dengan Menggunakan Model Eksponensial dan Logistik

This research was aimed to describe the application of differential equations of the population growth model in the City of Mataram, which is an exponential and logistic models for estimating the population of the City of Mataram in 2024. The research method used in this research is descriptive research with a qualitative approach carried out by observation and analyze the subject. The subject of this research was data on the population of the City of Mataram from 2006 to 2019. Meanwhile, to determine the accuracy and validity of the research data, the triangulation of sources was used. The data used comes from the Dispendukcapil and BPS the City of Mataram. The research result, it shows that the exponential model has an accuracy rate of 99,6%, which is very accurate, while for estimating with a logistic model each criterion is very accurate but the confidence level is 97,9%. Estimation results also show that population growth in the city of Mataram in the future will slowdown in its growth every 2 years, with an average decrease of 0.5%.

Assessing Population-Level Effects of Anthropogenic Disturbance on a Marine Mammal Population

The Population Consequences of Disturbance (PCoD) model is a conceptual framework used to assess the potential for population-level consequences following exposure of animals to a disturbance activity or stressor. This framework is a four-step process, progressing from changes in individual behavior and/or physiology, to changes in individual health, then vital rates, and finally to population-level effects. Despite its simplicity, there are few complete PCoD models available for any marine mammal species due to a lack of data available to parameterize many of the steps. Here, we present an application of the PCoD framework for migrating humpback whales exposed to a simulated commercial seismic survey scenario. We approached the framework in two ways; first, progressing sequentially forwards through the steps and basing our assessment on lactating females. This cohort was considered to be the most vulnerable in terms of energetic costs of disturbance, and most likely to influence any change in population growth due to future breeding success. Field measurements of behavioral responses of migrating humpback whales to seismic air guns from a previous study were used to parameterize an agent-based model (ABM). This ABM was used to estimate the probability of response, where a response was defined as a change in the migratory movement of female-calf pairs, and the duration of any resulting delay in migration. We then estimated the energetic consequences of any delay in migration for the lactating females and created population growth models with which to assess any population-level effects. The results of the forwards approach suggested a low potential for population consequences of seismic surveys on migrating humpbacks. Working backwards through the framework, we investigated “worst case” scenarios that could potentially lead to a population-level effect. Here, we started with increasing calf mortality and assumed that an exposure time greater than 48 h would increase mortality risk. We determined the most likely context in which this exposure would occur (resting area) and then tested this context within an ABM. This backwards approach illustrates how the PCoD model can be used to make management decisions regarding animal populations and exposure to anthropogenic stressors.

Population Growth Modeling via Rayleigh-Caputo Fractional Derivative

Population Growth Modeling via Rayleigh-Caputo Fractional Derivative

Accounting for sources of uncertainty when forecasting population responses to climate change.

In Focus: Jaatinen, K., Westerbom, M., Norkko, A., Mustonen, O., & Koons, D. N. (2021). Detrimental impacts of climate change may be exacerbated by density-dependent population regulation in blue mussels. Journal of Animal Ecology, 90, 562-573, https://doi.org/10.1111/1365-2656.13377. Conservation strategies for threatened species are increasingly dependent on forecasts of population responses to climate change. For such forecasts to be accurate, they must account for multiple sources of uncertainty, including those associated with projections of future climate scenarios and those associated with the models used to describe population dynamics. While many population forecasts incorporate parameter uncertainty in abiotic effects and process variance related to unexplained temporal variation, most forecasts overlook the importance of evaluating uncertainty in the structure of the population model itself. By accounting for structural uncertainties in a model of population growth for blue mussels, Jaatinen et al. (2021) demonstrated that density-dependent processes are likely to exacerbate adverse effects of climate change and reduce population viability of this keystone species. These findings highlight the importance of incorporating structural unknowns in population forecasts and the value of approaches that account for multiple sources of climate and model uncertainties. Forecasts that capture a range of possible population trajectories under climate change will help ensure efficient allocation of limited conservation resources.

Population growth model of Anadara granosa based on correlation between dimension of shell with the weight at the water environment of Sunda Strait

Exploitation of shellfish resources can affect its growth which can be seen from changes in the size of the shell dimensions including length, width and height. The study was conducted to determine the relationship between the dimensions of the shell with its total weight as a description of growth patterns, and to determine the environmental factors that affect shell growth. Descriptive method with direct observation technique was carried out at 3 observation stations in the Sunda Strait waters. Data were analyzed using power regression, while the correlation of environmental parameters were analyzed using PCA. The results show that the correlation between the dimensions of the shell and the total weight of the shell is allometric negative (b <3), which is an unbalanced growth between the dimensions of the shell and the weight of the shell, so that the shell growth pattern is indicated by the increase in width, length and height that was faster than the body weight. The parameters that affects the dimensions of the shell and weight are NH3-N, NO2-N, BOD, salinity, depth, TOM, brightness, Pb, Cd, Hg and temperature.

Exponential stability of integro-differential equations and applications

By a new approach, we get some new scalar criteria for the exponential stability of general nonlinear Volterra integro-differential equations. Then applications to models of biological population growth and Cohen–Grossberg neural networks are presented.

Invariant solutions of fractional-order spatio-temporal partial differential equations

Abstract This paper considers two categories of fractional-order population growth models, where a time component is defined by Riemann–Liouville derivatives. These models are studied under the Lie symmetry approach, and we reduce the fractional partial differential equations to nonlinear ordinary differential equations. Subsequently, solutions of the latter are determined numerically or with the aid of Laplace transforms. Graphical representations for integral and trigonometric solutions are presented. A key feature of these models is the connection between spatial patterning of organisms versus competitive coexistence.

COMPARISON OF VARIOUS FRACTIONAL BASIS FUNCTIONS FOR SOLVING FRACTIONAL-ORDER LOGISTIC POPULATION MODEL

Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms.

Forest management legacies affect demographics and population dynamics of spruce grouse in northern Maine

Conserving wildlife in managed forests requires knowledge of the interplay between species’ ecology and forestry practices. Spruce grouse (Falcipennis canadensis) are obligate residents of North American conifer forests with a southern range terminus in the northern U.S. We studied survival and reproduction of spruce grouse from 2012 through 2018 in north-central Maine, USA, within a landscape managed extensively for commercial forest products. We used radio telemetry data from 151 unique spruce grouse to monitor nest survival, brood success, and mortality of two age classes (juvenile and adult), and related these factors to a geospatial layer of stand harvest histories that provided a record of the timing and method of silvicultural treatments over the previous 30 years. We evaluated how demographic rates were affected by these forest practices, constructed stage-structured models of spruce grouse population growth, and used these models to quantify potential effects of management legacy on population dynamics. Nests in clearcuts with post-harvest treatments (herbicide and pre-commercial thinning) had lower success than those located in other stand types. Success of broods during summer increased with greater use of residual stands (unharvested for > 31 years), however, juvenile spruce grouse that made greater use of residual stands following independence had reduced survival. Adults that used a greater proportion of clearcuts lacking post-harvest treatments had the greatest annual survival. Deterministic and stochastic population models predicted values of λ < 1.0, suggesting population decline, and we found that λ was most sensitive and elastic to survival of adult females. Combined results from demographic analyses and our population model showed that greater use of untreated clearcuts by adult females had the largest potential to increase population growth, and that a stable to increasing growth rate (λ ≥ 1.0) could be achieved with particular combinations of stand use at different life stages. In this system the demographic mechanisms affecting relationships between forest management and spruce grouse population dynamics were complex. Ongoing changes in forest practices within the region may shift forests away from conifer-dominated composition, with negative consequences for the future status of the species.