A population growth model of Tetranychus urticae Koch (Acari: Tetranychidae)

This chapter reviews the basic mathematics of population growth as described by the exponential growth model and the logistic growth model. These simple models of population growth provide a foundation for the development of more complex models of species interactions covered in later chapters on predation, competition, and mutualism. The second half of the chapter examines the important topic of density-dependence and its role in population regulation. The preponderance of evidence for negative density-dependence in nature is reviewed, along with examples of positive density dependence (Allee effects). The study of density dependence in single-species populations leads naturally to the concept of community-level regulation, the idea that species richness or the total abundance of individuals in a community may be regulated just like abundance in a single-species population. The chapter concludes with a look at the evidence for community regulation in nature and a discussion of its importance.

This part of the book provides an introduction to some simple mathematical models that describe the growth of populations, and Quattro Pro and Excel spreadsheet programs are used to simulate these populations. The emphasis is on making a quantitative assessment of the consequences of Darwin's ‘overproduction of offspring’ and some aspects of ‘the struggle for existence’. Two basic types of population growth models are described. First, the consequences of Darwin's ‘overproduction’ of organisms are considered in Chapter 4, and described in mathematical terms using the geometric and exponential growth models. These models assume that there are no limits to the numbers of organisms and show that all populations growing in this manner will soon exhaust the earth's resources. Second, in Chapter 5 we look at one aspect of Darwin's ‘struggle for existence’, intraspecific competition, which occurs when a population grows in an environment of finite size. This form of growth is described using the logistic, or sigmoid, growth model, which has some rather restrictive assumptions. This basic model is then modified to assess the effects of time lags and environmental variation on the form of population growth. The models are applied to laboratory and field data show how they relate to reality.

The classical population growth models include the Malthus population growth model and the logistic population growth model, each of which has its advantages and disadvantages. To address the disadvantages of the two models, this paper establishes a grey logistic population growth prediction model, based on the modeling mechanism of the grey prediction model and the characteristics of the logistic model, which uses the least-squares method to estimate the maximum population capacity. In accordance with the data characteristics of population growth, the weakening buffer operator is used to establish the weakening buffer operator grey logistic population growth prediction model, which improves its accuracy, thus improving the classic population prediction model. Four actual case datasets are used simultaneously, and the two classical grey prediction models are compared. The results of the six evaluation indicators show that the effects of the new model demonstrate obvious advantages. Finally, the new model is applied to the population forecast of Chongqing, China. The prediction results suggest that the population may reach a peak in 2020 and decline in the future. This finding is consistent with the logistic population growth model.

Dynamical behaviour of discrete logistic equation with Allee effect in an uncertain environment

This paper reviews two population growth models and tries to find out a proper way to explain and predict population growth. It shows that the exponential growth model and logistic growth model should not be used to predict population growth. The paper highlights the difference between human population growth and biological population growth and analyzes factors affecting population growth based on data available. Evidence from time series analysis indicates that, two factors, the degree of urbanization and the sex ratio, have significant influences on population growth in China.

Reliable estimates of population growth rates and densities are fundamental for effective wildlife management programs. We assessed the precision of spotlight-counting as a technique to monitor changes in rabbit abundance by fitting simple population growth models to observed trends in spotlight-count data during an 18-month period of increase in European rabbit (Oryctolagus cuniculus) abundance at sites in North Canterbury, New Zealand. A model-selection approach identified a simple exponential population growth model, allowing the observed rate of increase to differ between spring-summer (Aug-Feb) and autumn-winter (Mar-Jul) to be an adequate description of the observed data. The exponential rate of increase (r) over the study period differed markedly between spring-summer and autumn-winter periods, and averaged 2.3 yr -1 and 2.5 yr -1 for the 2 sites monitored. We used the fitted exponential model to estimate the observation error per spotlight transect. The estimated coefficient of variation for 1 night of counting of 10-km transects was 16%. With such data and model assumptions, only a modest number of surveys would be required to detect, with a high degree of certainty, moderate changes in spotlight-count indices of rabbit abundance either by analysis of variance or log-linear regression.

Incorporating Spatial Variation in Density Enhances the Stability of Simple Population Dynamics Models

Some methods for demographic inference based on the observed genetic diversity of current populations rely on the use of summary statistics such as the Site Frequency Spectrum (SFS). Demographic models can be either model-constrained with numerous parameters, such as growth rates, timing of demographic events, and migration rates, or model-flexible, with an unbounded collection of piecewise constant sizes. It is still debated whether demographic histories can be accurately inferred based on the SFS. Here, we illustrate this theoretical issue on an example of demographic inference for an African population. The SFS of the Yoruba population (data from the 1000 Genomes Project) is fit to a simple model of population growth described with a single parameter (e.g., founding time). We infer a time to the most recent common ancestor of 1.7million years (MY) for this population. However, we show that the Yoruba SFS is not informative enough to discriminate between several different models of growth. We also show that for such simple demographies, the fit of one-parameter models outperforms the stairway plot, a recently developed model-flexible method. The use of this method on simulated data suggests that it is biased by the noise intrinsically present in the data.

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Population growth models typically incorporate attributes observable at the population scale, often overlooking the trade-off between individual-level reproductive and behavioral traits and their influence on population size. Individuals' survival and reproductive abilities are expected to dynamically evolve depending on the population size, which is affected by the aggregation of individual decisions. Reconciling individual-level incentives with population-level dynamics requires an integrative framework that explicitly addresses the intertwined relationships between population growth and individual decision-making processes. We formulate a multiscale modeling framework that integrates the logistic population growth model with an optimal foraging model to study the interplay between individual-level behavioral incentives and population growth dynamics. Specifically, we explicitly model individuals' decision-making process, which shapes their reproductive fitness and, ultimately, influences population growth. Moreover, we incorporate the concept of resource limitations from the logistic growth model to account for dynamic incentives that depend on population size. Our results yield insights into the multiscale processes, such as the selection pressure of behavioral choices and the cost-benefit of social activities that influence population robustness beyond mere size and aggregated reproductive traits. We found that populations exhibiting similar limiting sizes may undergo significantly different transient dynamics. This variation may be induced by environments imposing distinct behavioral cost-benefit trade-offs that require individuals to exert different levels of foraging effort to maintain reproductive viability.

This study models the prevalence and fatality of the Covid-19 pandemic in Nigeria from February 2020 to July 2022. It is a comparative study of two prominent models: The Gompertz and Logistic population growth models. The data for this study was obtained from the website of Our World in Data, OWID (https//www.ourworldindata.org). The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were employed to compare the performance of the models, and the number of iterations before convergence and convergence tolerance for each model was also put into consideration. The study revealed that the Gompertz population growth model provides a better fit compared to the logistic growth in modelling the cumulative covid-19 cases and cumulative covid-19-related deaths in Nigeria. From the models, we obtained important features of the pandemic, such as the growth rate and asymptotes.

The logistic growth model with proportional harvesting is a population growth model that takes into account harvesting factors. In real life, not all conditions can be known with certainty, such as different growth rates in each population and harvest rates depending on the needs of the harvester. To overcome these conditions, there is a concept that accommodates the problem of uncertainty, namely the fuzzy concept. This concept can be induced into a logistic model with proportional harvesting which assumes the intrinsic growth rate and the harvest rate is expressed by fuzzy numbers. The purpose of this research is to form a logistic model with fuzzy proportional harvesting, analyze the stability of the model, and form a numerical simulation. This study uses the alpha-cut method to generalize the intrinsic growth rate and harvest rate from crisp numbers to fuzzy numbers, then the Graded Mean Integration Representation (GMIR) method to defuzzify the model, and the linearization method to analyze the stability of the model. The results of this study obtained a logistic model with proportional harvesting. Then the model was developed into a logistic model with fuzzy proportional harvesting by assuming the intrinsic growth rate and the harvest rate expressed by fuzzy numbers. From the model obtained 2 equilibrium points, namely the first equilibrium point is unstable and the second equilibrium point is asymptotically stable under certain conditions. Model simulation is given to show illustration of stability analysis. From the simulation, it can also be shown that the higher the graded mean value, the lower the population.

Richards model, Gompertz model, and logistic model are widely used to describe growth model of a population. The Richards growth model is a modification of the logistic growth model. In this paper, we present a new modified logistic growth model. The proposed model was derived from a modification of the classical logistic differential equation. From the solution of the differential equation, we present a new mathematical growth model so called a WEP-modified logistic growth model for describing growth function of a living organism. We also extend the proposed model into couple WEP-modified logistic growth model. We further simulated and verified the proposed model by using chicken weight data cited from the literature. It was found that the proposed model gave more accurate predicted results compared to Richard, Gompertz, and logistic model. Therefore the proposed model could be used as an alternative model to describe individual growth.

The biggest challenge in the world is population growth and determining how society and the state adapt to it as it directly affects the fundamental human rights such as food, clothing, housing, education, medical care, etc. The population estimates of any country play an important role in making the right decision about socio-economic and population development projects. Unpredictable population growth can be a curse. The purpose of this research article is to compare the accuracy process and proximity of three mathematical model such as Malthusian or exponential growth model, Logistic growth model and Least Square model to make predictions about the population growth of Bangladesh and India at the end of 21st century. Based on the results, it has been observed that the population is expected to be 429.32(in million) in Bangladesh and 3768.53 (in million) in India by exponential model, 211.70(in million) in Bangladesh and 1712.94(in million) in India by logistic model and 309.28 (in million) in Bangladesh and 2686.30 (in million) in India by least square method at the end of 2100. It was found that the projection data from 2000 to 2020 using the Logistic Growth Model was very close to the actual data. From that point of view, it can be predicted that the population will be 212 million in Bangladesh and 1713 million in India at the end of the 21st century. Although transgender people are recognized as the third sex but their accurate statistics data is not available. The work also provides a comparative scenario of how the state has adapted to the growing population in the past and how they will adapt in the future.

Populations live in habitats whose quality varies spatially and temporally. Understanding how populations deal with these variable habitats can aid our understanding of theoretical issues, and practical issues of biological invasions and biodiversity conservation. I investigate these issues by superimposing simple models of population growth and dispersal on spatiotemporally fractal landscapes, and examining the properties of the landscapes, and of the populations inhabiting them. The properties of the simulated landscape sequences are comparable to those of real habitats. The simulated populations exhibit a range of dynamic behaviors; these behaviors are strongly influenced by the fractal parameters of the landscapes. The results may help explain several important phenomena seen in reintroductions of threatened and endangered species, introductions of biological control agents, and biological invasions. These phenomena include frequently observed lags between population introduction and initial population growth and spread, and the observed high frequency of failure of introductions.